Question

1. Prove that V5 is irrational
2. Prove that 3+215 is irrational.
3. Prove that the following are irrationals:
( I ) 1/root 2
(ii) 7 root 5
(iii) 6+ root 2
Plz solve this quickly it's very important now I will mark u as brain list plz friends help me ​

Answer 1

Answer:

Step-by-step explanation:

1) Say, √5 is a rational number. ∴ It can be expressed in the form p/q where p,q are co-prime integers. ... Therefore, p/q is not a rational number. This proves that √5 is an irrational number.

2) let 3+√215 be rational no.

3+√215=p/q

∴√215=p/q-3     ----(1)

now,p/q is a rational no.

then,p/q-3 is also a rational no.

then,√215 is a rational no.      ----from(1)

but,it contradicts the fact that√215 is an irrational no.

∴√215≠p/q-3

∴our assumption is wrong.

hence,3+√215 is an irrational no.

3)1√2=let 1√2 be a rational no.

∴1√2=p/q

∴√2=p/1q    ----(1)

∴now ,p/q is a rational no. then p/1q is also rationalk no.

then ,√2 is a rational no.     ----from(1)

but ,√2 is an irrational no.

∴√2≠p/1q

∴our assumption is wrong.

hence ,1√2is an irrational no.

(2),(3) just do like the above method